Algebra-2

According to the Rational Root Theorem, for a polynomial equation , the possible rational roots are of the form , where is a factor of the constant term and is a factor of the leading coefficient .

 

For the equation , the leading coefficient is 5 and the constant term is 10.

 

Factors of 10 are ±1, ±2, ±5, ±10.

Factors of 5 are ±1, ±5.

 

So the possible rational roots are ±1/1, ±1/5, ±2/1, ±2/5, ±5/1, ±5/5 (which simplifies to ±1), ±10/1, ±10/5 (which simplifies to ±2).

 

Now we test these possible roots one by one.

 

Testing :

Substitute into the equation: .

 

Testing :

Substitute into the equation: .

 

Testing :

Substitute into the equation: